Interest Rates in Trade Credit Markets

Interest Rates in Trade Credit Markets Klenio Barbosa Humberto Moreira Walter Novaes April 2009 Abstract Despite strong evidence that suppliers of inputs are usually informed lenders, the cost of trade credit rarely varies with borrowing firm characteristics. We solve this puzzle by demonstrating that it is optimal for suppliers to keep riskier firms indifferent between trade credit and loans from uninformed banks. Because these bank loans are likely to vary across industries but not with firm characteristics, the same pattern applies to the cost of trade credit. The model predicts that the cost of trade credit is more likely to vary with firm characteristics in industries that are plagued by moral hazard problems or economic distress. JEL: G30, G32 Key Words: Trade Credit; Information; Credit Risk. Toulouse School of Economics. E-mail: klenio.barbosa@tse-fr.eu Graduate School of Economics-FGV. E-mail: humberto@fgv.br Department of Economics at PUC-Rio. E-mail: novaes@econ.puc-rio.br

1 Introduction In the G7 countries, suppliers of inputs to production processes extend a significant amount of credit to their customers. 1 Smith (1987), Mian and Smith (1992) and Biais and Gollier (1997) argue that the prominence of trade credit is due to an informational advantage: The sales effort of suppliers makes it easier for them to assess their customers credit risk. Accordingly, Petersen and Rajan (1997) show that, vis-à-vis banks, suppliers extend more credit to firms with current losses and positive growth of sales; a finding that they interpret as a supplier s comparative advantage in identifying firms with growth potential. Nevertheless, Giannetti, Burkart and Ellingsen (2008) show that credit risk is not an important determinant of interest rates in the U.S. trade credit markets. Apparently, the cost of trade credit varies across industries but not with firm characteristics. 2 This result is hard to reconcile with the evidence that suppliers are informed lenders. After all, basic economic principles suggest that interest rates should increase with the borrower s risk of credit. We solve this puzzle by arguing that competition with uninformed banks makes it difficult for suppliers to align the cost of trade credit with their customers risk. In particular, an attempt to selectively raise the interest rates paid by the riskier firms will induce them to borrow from uninformed banks, whose interest rates overestimate the odds that the debt contract will be honored. We demonstrate that it is optimal for suppliers to keep the riskier firms indifferent between trade credit and loans from uninformed banks. Because the cost of these bank loans is likely to vary across industries but not with firm characteristics, the same pattern applies to the cost of trade credit. To understand the main ideas of our paper, consider an industry with a continuum of firms, a bank, and a supplier of inputs. The firms seek financing to undertake a profitable project, whose possible outcomes are two: a positive return on the investment (success) or not (failure). While a bank loan is the standard source of financing, trade credit is a more efficient alternative because the supplier has an informational advantage over the bank. 1 See Rajan and Zingales (1995) for the importance of trade credit in the G7 countries (Canada, France, Germany, Italy, Japan, U.K., and the U.S.). 2 See Ng, Smith and Smith (1999) and Petersen and Rajan (1994). 1

To model the supplier s informational advantage, we assume that the probability that the project succeeds depends on firm-specific risk factors the types that are distributed in the positive interval [t, 1]. Without loss of generality, the probability of success of a type-t firm, p t, increases with t. When firms seek financing to undertake a project, they already know their types and so does the supplier. The bank, on the other hand, does not know the types. Will the supplier take advantage of its private information to vary the cost of trade credit with the firm-specific risk factors? To answer this question, we build upon a key observation: knowledge of the borrowing firms types gives market power to the supplier. As suggested by standard monopoly pricing, a sufficiently inelastic demand for inputs (and, by extension, for credit) makes it optimal for the supplier to raise the cost of trade credit until it reaches the maximum level that firms are willing to accept, that is, the interest rate charged by the uninformed bank. 3 Since the interest rates of these bank loans cannot vary with information that is privy to the supplier, the cost of trade credit contracts that mimic the bank loans cannot either. Accordingly, we demonstrate that the unique equilibrium of our model implies that the cost of trade credit does not vary with firm characteristics, if the elasticity of the demand for inputs is below a certain threshold ɛ. If the elasticity of demand is larger than ɛ, then it is not optimal for the supplier to offer all firms the same terms of trade credit. Instead, the supplier induces a larger volume of loans to its most valuable customers the safer firms by offering them lower interest rates. As such, the equilibrium splits the firms into two groups: The riskier ones pay the bank rate while the safer firms pay lower interest rates that decrease with their probability of success. This implication is interesting, for at least two reasons. First, an equilibrium in which the cost of trade credit is the same for all firms is extreme. As Ng, Smith and Smith (1999) point out, suppliers occasionally waive penalties for late payments. For all practical purposes, waving penalties is equivalent to selectively reducing the cost of trade credit. Second, and more importantly, models of interest rates in trade credit markets should yield some conditions under which the cost of trade credit does vary with firm characteristics. The equilibrium that allows for trade credit contracts to vary with firm characteristics can occur under at least two 3 Brennan, Maksimovic and Zechner (1988) also argue that the elasticity of the demand for inputs determines the cost of trade credit. In their model, the supplier is a monopolist in the product market. 2

phenomena of this sort are present: economic distress and moral hazard problems. Economic distress reduces the expected debt repayment, inducing the bank to increase interest rates. In turn, the higher bank rate lets the supplier raise the cost of trade credit, thereby increasing the margins of profit of trade credit transactions. Large margins make the volume of loans more important for the supplier, strengthening its incentive to reduce the interest rate paid by the safer firms. As a result, our model predicts that the cost of trade credit is more likely to vary with firm characteristics in economically distressed industries. A similar argument predicts that the cost of trade credit is more likely to vary with firm characteristics in industries plagued by moral hazard problems. As Burkart and Ellingsen (2004) argue, suppliers can mitigate moral hazard problems more efficiently than banks, because trade credit is extended in kind rather than cash. It then follows that moral hazard problems weaken the bank s ability to compete with the supplier, implying higher margins of profit in trade credit transactions and stronger incentives for the cost of trade credit to vary with the borrower s risk. Moral hazard, therefore, doesn t explain the existing evidence on interest rates in trade credit markets, although it may lead trade credit to be efficient. This paper builds primarily on Biais and Gollier (1997) and Burkart and Ellingsen (2004), whose main goal is to explain why trade credit is pervasive. In Biais and Gollier, suppliers can identify firms whose credit risk is overestimated by banks. Knowing that these firms credit lines are unduly low, suppliers are willing to fill their financing needs. Burkart and Ellingsen s paper argues that loans in kind (as opposed to cash) are less vulnerable to moral hazard problems. As such, suppliers may extend credit to firms that have exhausted their ability to borrow from banks. In Biais and Gollier as well as Burkart and Ellingsen s models, the cost of trade credit would vary with the suppliers private information, were the customers to have different levels of credit risk. The remainder of the paper is organized as follows. Section 2 describes the basic model, which assumes that the supplier s informational advantage is the reason for trade credit to exist. Section 3 shows how industry characteristics and firm-specific risk factors determine the cost of trade credit. Section 4 introduces moral hazard and shows that it makes the cost of trade credit more sensitive to firm characteristics. Section 5 discusses the robustness of 3

the results to different information structures and richer trade credit contracts, and Section 6 concludes. Proofs that are not in the text can be found in the appendix. 2 The Model 2.1 Sequence of events and information structure Consider a risk-neutral economy with a zero risk-free rate, a bank, a supplier of inputs, and a continuum of firms in the interval [t, 1], where t > 0. In this economy, the firms seek financing to undertake a project, whose possible outcomes are only two; they yield a positive return on the investment (success) or not (failure). When we add firm-specific factors to those that are intrinsic to the project, the probability of success increases with the firm s type, that is, p t = tp, with p (0, 1) and t [t, 1]. While a bank loan is the standard source of external financing, trade credit is efficient in our model because the supplier knows the firms types, but the bank doesn t. Neither the bank nor the supplier can observe the project s return without bearing a verification cost, though. As Townsend (1979) and Gale and Hellwig (1985) demonstrate, verification costs imply that outside equity isn t an optimal financing contract. Hence, firms rely on debt-like instruments to finance the project, whether the lender is the bank or the supplier. Figure 1: Timing of events 0 1 2 3 Firms seek financing Supplier and bank may offer credit Financing decision/ Purchase of inputs Production/ Payoffs As figure 1 shows, the game begins at date 0, when the firms seek financing to purchase inputs for the project. At this time, they already know their types, and so does the supplier. 4

In contrast, the bank knows only the cumulative distribution of types, F 0 (t), and the projectspecific risk factor, p, which is common knowledge. 4 In addition to allowing a better assessment of the firms credit risk, the informational advantage gives the supplier a first-mover advantage: We assume that the supplier makes a take-it-or-leave-it offer at date 1, whenever it is in its interest to extend trade credit. 5 When making trade credit offers, the supplier knows that the bank may also offer credit. The financing decision ends with a bank loan at date 2 if the firm either declines a trade-credit offer or trade credit isn t available. In any event, we assume that the bank does not observe the terms of the trade credit offers, but we let it update the distribution of types, once a firm agrees to take a bank loan. After securing the funds, the firms buy the inputs and undertake the project at date 2. The payoffs realize at date 3, when the firms repay the debt (if possible) and distribute the residual cash flow to shareholders. 2.2 Technology In our model, there are only two possible outcomes for the project: success or failure. In case of success, the return of investing I is Q(I). The production function Q(I) is increasing and strictly concave on the investment, satisfying Q(0) = 0 and the standard Inada conditions. 6 In contrast, failure destroys the return on the investment. Frank and Maksimovic (1998) argue that suppliers are more efficient than banks in rescuing the assets of financially distressed firms. 7 As such, we let the project s salvage value (net of the verification cost) vary with the source of external financing. For simplicity, we assume that the bank cannot rescue the inputs in default, while the supplier rescues a fraction δ [0, 1] of the investment in inputs. If δ = 0, then the supplier does not have an advantage over the bank in default. 4 See Petersen and Rajan (1997) and McMillan and Woodruff (1999) for empirical evidence that suppliers have an informational advantage over banks in the U.S. and in Vietnam, respectively. 5 The main results of our paper hold under less extreme assumptions on how the supplier and the firms reach an agreement over the terms of trade credit. 6 The Inada conditions are lim I 0 Q (I) = and lim I Q (I) = 0. 7 Petersen and Rajan (1997) find evidence that loans to bad lenders are more costly for banks than suppliers, because it is easier for the latter to transform repossessed inputs into liquid assets. 5

2.3 Loan contracts We assume that free entry rules out abnormal profits for the uninformed bank; any attempt to extract rents from the firms attracts new (uninformed) lenders. Of course, the break-even payment depends on the firm s type. In particular, riskier firms should pay more, conditional on the project s success. We claim that, in our model, the bank cannot screen the firms types. To see why, consider any two standard debt contracts, (I k, A(I) k ) k {T, ˆT }, that finance I k in exchange for a promised payment A(I) k. 8 For the bank to screen some of the firms, there must exist types t T and ˆt ˆT such that (I T, A(I) T ) gives a larger expected profit for t than the contract (I ˆT, A(I) ˆT ), with the reverse inequality for the type ˆt, that is, p t [Q(I T ) A(I T )] > p t [Q(I ˆT ) A(I ˆT )] and pˆt [Q(I T ) A(I T )] pˆt [Q(I ˆT ) A(I ˆT )]. These two conditions cannot hold simultaneously, though, because p t [Q(I T ) A(I T )] > p t [Q(I ˆT ) A(I ˆT )] implies that p t [Q(I T ) A(I T )] > p t [Q(I ˆT ) A(I ˆT )] for any t t. Hence, if a loan contract is optimal for a type-t firm, then it is also optimal for the other types, thereby preventing the bank from designing a screening device. This feature of the model preserves the supplier s informational advantage, which is crucial to the purpose of our paper, while allowing for risk characteristics to vary across firms. 9 It then follows that the amount of a bank loan request does not update the bank s prior over the borrower s type; the updating is restricted to the firm s willingness to use the bank as the source of external financing. Here, we take the updated distribution, F 1 (t), as given. 10 Because the bank cannot rescue assets in default, the zero profit condition on a standard debt contract (I, A(I)) is thus pe 1 [t]a(i) = I, or equivalently: with pe 1 [t] = p 1 tdf t 1(t). r B A(I) I 1 = 1 1, (1) pe 1 [t] 8 Townsend (1979) demonstrates that verification costs make a standard debt contract optimal for the bank. 9 Intuitively, our economy should be interpreted as an industry, whose firms opt for the same production plan but differ with respect to their ability to manage the production process. 10 Proposition 2 characterizes the updated distribution F 1 (t). 6

Equation (1) implies that the promised payment, A(I), varies with the loan amount, I, but the interest rate on the loan doesn t: r B = 1 pe 1 [t] 1 for any I. To characterize the optimal loan contract it thus suffices to pin down the loan amount that maximizes the value of a representative firm that borrows from the bank, that is, the investment I E 1[t] that makes the marginal productivity of investment, pe 1 [t]q (I E 1[t] ), equal to its marginal cost, 1. The necessary and sufficient condition that characterizes the optimal investment is thus Q (I E 1[t] ) = 1 pe 1 [t]. (2) The optimal loan contract, therefore, lends I E 1[t], in exchange for the borrower s promise to pay (1 + r B )I E 1[t] after the project s payoff realizes. As it turns out, the optimal loan contract can be implemented by a linear debt contract that lets the firms pick the loan amount. To see this, consider the maximization problem that yields the optimal investment of a type-t firm that finances the inputs at an interest rate r: ] max p [Q(I) t (1 + r)i. (3) I The objective function (3) takes into account that the firm benefits from the project only if it succeeds. With probability 1 p t the firm gets into operational problems that destroy the project s returns. The first order condition of program (3), which is also sufficient, is Q (I ) = 1 + r. (4) Plugging the bank rate r B = 1 pe 1 [t] 1 into the first order condition (4) yields Q (I ) = 1 pe 1 [t]. But this is exactly the first order condition (2) for the value-maximizing investment of the type E 1 [t]. Without loss of generality we can thus focus the analysis of bank loans on linear debt contracts at the interest rate r B = 1 pe 1 [t] 1. 2.4 Trade credit We consider a supplier endowed with a constant return-to-scale technology in a market for inputs without barriers to entry. To simplify the notation, we assume that the constant marginal cost of production is one, which is also the equilibrium price of the input. As a result, the supplier does not fetch abnormal profits in the product market. 7

Nonetheless, the informed supplier is the only lender who can vary the loan contracts with the borrowing firm s type. Due to this informational advantage, it can enjoy abnormal profits in trade credit transactions. The supplier s problem, therefore, is to maximize its expected financial profits, while taking into account that firms can borrow from the bank at the interest rate r B = 1 pe 1 1. When solving this problem, we shall restrict our attention to linear debt [t] contracts: The supplier makes a take-it-or-leave-it offer to finance purchases of inputs at an interest rate r t that may vary with the firm s type t. Linear debt contracts are pervasive in trade credit markets. For instance, a common trade credit contract in the U.S. combines a 30 day maturity with a two percent discount for early payment within 10 days of the invoice (2-10 net 30 loans). As Petersen and Rajan (1997) point out, not exercising the discount option is equivalent to accepting a 10-day debt contract at an interest rate of 44 percent a year. Assuming linear contracts from the onset may thus be interpreted as a short-cut to focus our attention on the most relevant determinants of interest rates in standard trade credit transactions. 11 3 Equilibrium in the trade credit market This section is divided in three parts. In the first, we derive the optimal trade credit contracts, taking as given the bank rate r B. In the second part, we characterize the equilibrium of the game by deriving the posterior belief F 1 (t) that determines r B. The last part of the section then shows how economic shocks and industry characteristics (i.e., the salvage value δ) affect the likelihood that the cost of trade credit varies with firm characteristics. 11 Section 5 demonstrates that the main insight of our paper i.e., competition prevents informed suppliers from aligning the cost of trade credit with the borrower s risk is robust to optimal nonlinear contracts, if default imposes small economic losses on suppliers. 8

3.1 The optimal trade credit contracts The goal of the supplier is to design a linear debt contract that maximizes its expected financial profits. The optimal interest rate r t of a trade credit transaction with a type-t firm solves ( ) max p t (1 + r t ) + (1 p t )δ 1 I (r t ) (5) r t ( 1 ) subject to (1 δ) p 1 r t r B. (6) t The objective function is the supplier s expected profit from extending trade credit to a t-firm at an interest rate r t. The interest rate determines the firm s investment in the project, I (r t ), from the first order condition (4). With probability p t, the firm can pay principal plus interest: (1 + r t )I (r t ). But, with probability 1 p t (0, 1), the firm experiences operational problems that destroy the project s return, leaving only a salvage value (net of the verification costs): δi (r t ). In any event, the supplier bears the cost of the input. The constraint (6) summarizes the two restrictions faced by the supplier. First, the interest ( ) rate r t 1 must be larger than or equal to the supplier s break-even point: (1 δ) 1. The p t interest rate cannot be too high, though, or else the firm is better off borrowing from the bank. As such, the bank rate r B is the maximum cost of trade credit. The only reason for a solution to Program (5) not to exist is the upper bound on the interest rate (r t r B ). It isn t profitable for the supplier to offer trade credit, if the bank ( ) rate r B 1 is lower than the supplier s break-even point, (1 δ) 1. If so, the program s p t opportunity set is empty, meaning that the supplier will not offer trade credit to the type-t firm. Using that p t = tp, a necessary and sufficient condition for trade credit to the type-t ( firm to be profitable for the supplier is r B 1 (1 δ) ), 1 or equivalently tp t t(δ) = 1 δ p(1 δ + r B ). (7) Having determined the types to whom the supplier has incentive to offer trade credit, our next task is to characterize the interest rate r t that solves the supplier s maximization problem ( ) 1 (5). To do this, note first that the interest rate (1 δ) 1 is not optimal for the supplier, p t regardless of the firm s type. This interest rate yields zero expected profits for the supplier, 9

while any slightly larger rate implies strictly positive expected profits. 12 The optimal interest ( ) 1 rate, therefore, either satisfies (1 δ) 1 < r t < r B or is the bank rate r B. p t A standard trade-off, between margin of profit and volume of sales, determines the optimal interest rate. On the one hand, raising the interest rate increases financial profits per unit of trade credit. On the other hand, it decreases the demand for inputs. To rule out the uninteresting case that it is always optimal for the supplier to raise the cost of credit as much as possible, we assume: 13 Assumption 1 Let ɛ(r) = Thus, ɛ(r) is non-decreasing in r. di (r) (1+r) dr I (r) be the interest-elasticity of the demand for inputs. Given Assumption 1, Proposition 1 demonstrates that the interest-elasticity of the demand for inputs solves the trade off between margin and volume. Proposition 1 It is profitable for the supplier to offer trade credit if and only if the firm s type is t t(δ). In this case, the optimal interest rate is r t = r B if and only if ɛ(r B ) ɛ(r B, δ, t) with ɛ(r t, δ, t) = tp(1+r t ) tp(1+r t δ) (1 δ). If ɛ(rb ) > ɛ(r B, δ, t), then (1 δ) ( 1 p t 1 ) < r t < r B, with r t strictly decreasing in δ and t, unless δ = 1, in which case r t does not vary with t. Proposition 1 shows that the supplier raises the interest rate to its upper bound, if and only if the demand for inputs is sufficiently inelastic at the bank rate r B, that is, ɛ(r B ) ɛ(r B, δ, t). More interestingly, Proposition 1 also shows that the optimal interest rate r t increases with the firm s risk, with two exceptions: If default does not impose an economic loss (δ = 1) or if r t reaches the maximum interest rate that firms are willing to pay, that is, the bank rate r B. 3.2 Equilibrium contracts From Proposition 1, the cost of trade credit of a type-t firm does not vary with its probability of success, whenever the elasticity at the bank rate, ɛ(r B ), is smaller than or equal to the 12 More formally, the unit profit, p t (1 + r t ) + (1 p t )δ 1, strictly increases with r t, and, from the Inada condition, I (r t ) is always positive for any r t slightly larger than the break-even rate. 13 The assumption holds, for example, if Q(I) = I α with α (0, 1). 10

cutoff ɛ(r B, δ, t). The elasticity of the demand for inputs, therefore, is a key determinant of the interest rates in the trade credit markets. As one can check, the cutoff ɛ(r B, δ, t) decreases with the firm s type, t. Hence, a sufficient condition for the optimal trade credit contracts not to vary with firm characteristics is ɛ(r B ) ɛ(r B, δ, 1). If this elasticity condition is not satisfied and default is costly (i.e., δ < 1), then at least some trade credit contracts prescribe interest rates that fall with the borrowing firm s probability of success. Whether the cost of trade credit varies with firm characteristics thus depends on how elastic the demand for inputs is. As it turns out, Petersen and Rajan (1997) show that, in the U.S., the demand for trade credit seems to be fairly inelastic; a finding that our model relates to interest rates that do not vary with firm characteristics. Ng, Smith and Smith (1999) also show, however, that some firms keep the discount for early payments, despite missing the contractual deadline. all practical purposes, waiving the deadline for discounts is equivalent to selectively reducing the cost of trade credit. For A testable model of interest rates in the trade credit markets, therefore, should yield implications on the likelihood that the cost of trade credit varies with firm characteristics. These implications can be drawn from our model, because Proposition 2 links the equilibrium interest rates not only to the elasticity of demand but also to industry characteristics. Proposition 2 There is a unique sequential equilibrium of the game. In this equilibrium, the strategies and beliefs are: Bank: Offers to all firms loan contracts at an interest rate r B = 1 pe 1 [t] 1, where E 1 [t] = 1 tdf t 1(t). Firms: If the type-t firm has access to trade credit at an interest rate r t r B, then it borrows I (r t ) from the supplier. Otherwise, the t-firm borrows I (r B ) from the bank to purchase inputs for the project. Supplier: Offers a trade credit contract (r t, I (r t )) to all firms. There exists ˆt [t, 1] such that t ˆt implies r t = r B, and t > ˆt implies r t = r(δ, t) ( (1 δ) ( 1 p t 1 ), r B), with r(δ, t) decreasing in δ and t. The cutoff type is ˆt = 1 if ɛ(r B ) ɛ(r B, δ, 1), and 11

ˆt = t if ɛ(r B ) ɛ(r B, δ, t). If ɛ(r B, δ, 1) < ɛ(r B ) < ɛ(r B, δ, t), then ˆt is implicitly defined by ɛ(r B ) = ɛ(r B, δ, ˆt), with ˆt (t, 1). Beliefs: P rob(t = t bank loan) = 1, which implies F 1 (t) = 1, t [t, 1]. In our model, there is no economic reason for the uninformed bank to finance the purchase of inputs; the supplier s first-mover advantage lets it displace the bank. Accordingly, Proposition 2 demonstrates that a firm s request for a bank loan is an event off the equilibrium path: All firms use trade credit. Because a bank loan is off the equilibrium path, Bayes rule does not pin down the updating of the bank s prior upon a request for bank loan. The proof of Proposition 2 shows, nonetheless, that a distribution concentrated on the t-type is the only updated belief that satisfies the consistency requirement of sequential equilibrium (Kreps and Wilson (1982)). The bank, therefore, interprets a request for a loan as a signal that the firm is the riskiest type t, setting the interest rate according to this belief, that is, r B = 1 pt 1.14 More importantly, Proposition 2 characterizes the equilibrium of the game through a cutoff type ˆt that splits the firms in two groups: The safer firms, t > ˆt, pay an interest rate r t < r B that decreases with their probability of success, while the riskier ones, t ˆt, pay the bank rate r B that does not vary with firm characteristics. If ɛ(r B ) ɛ(r B, δ, 1), then ˆt = 1, implying that the cost of trade credit is r B for all firms. The safer firms pay an interest rate lower than r B, though, if ɛ(r B ) > ɛ(r B, δ, 1), in which case ˆt < 1. In particular, a sufficiently elastic demand (ɛ(r B ) > ɛ(r B, δ, t)) implies that the cost of trade credit always falls with the firm s probability of success, that is, ˆt = t. The characterization of the equilibrium of the game implies that the cutoff type ˆt is a sufficient statistic for the sensitivity of the cost of trade credit with respect to firm-specific risk factors. As the cut-off type ˆt decreases, there is an increase in the fraction of trade credit contracts whose interest rates fall with the firm s probability of success. The next section builds on this result to show how industry characteristics shape the likelihood that the cost 14 Intuitively, the riskier types are denied trade credit in any perturbation that makes a bank loan a positive probability event. As the perturbation goes to zero, the beliefs converge to a mass at t, which is thus the unique updated belief that satisfies the Kreps-Wilson refinement. 12

of trade credit varies with firm characteristics. 3.3 The likelihood that the cost of trade credit varies with firm characteristics Typically, interest rates in the trade credit markets vary across industries but not with firm characteristics. As such, a test with the power to reject our model should be centered around implications that help predict when or where the cost of trade credit varies with firm characteristics. In this spirit, our model yields potentially testable implications that link the cross-sectional variation of interest rates to the salvage value of the project, δ, and the state of the economy. As the salvage value of the project goes up, so does the supplier s expected return on a trade credit contract. Large margins make the volume of loans more important for the supplier, strengthening its incentive to use the risk of credit to price discriminate its customers. By better aligning the interest rates with the credit risk, the supplier can increase the margins of the riskier trade credit contracts, while inducing larger loans to its most valuable customers, the safer firms. Accordingly, a larger fraction of trade credit contracts should vary with the firm s probability of success. Proposition 3 formalizes this intuition. { ( Proposition 3 Define δ 1 p(1+r B ) 1 p 1 1 r B ) } +1 and δ { ( 1 tp(1+r B ) 1 tp 1 1 r B ) } +1. The cost of trade credit does not vary with firm characteristics if δ δ, while it always falls with the firm s probability of success if δ [ δ, 1). If δ < δ < min{ δ, 1}, the fraction of firms for whom the cost of trade credit falls with the probability of success increases with δ. Petersen and Rajan (1997) show that suppliers extend less credit in industries that keep a high fraction of finished goods in inventory; a finding that they interpret as evidence that it is easier for suppliers to transform repossessed inputs (rather than finished goods) into liquid assets. As such, Proposition 3 predicts that a high fraction of finished goods decreases the likelihood that the cost of trade credit varies with firm characteristics. Consider now an economic shock that reduces the probability of success of all firms, that is, the support of types shifts from [t, 1] to [t min, t max ], with t min < t and t max < 1. After the 13

shock, the distribution of types changes from F 0 (t) to G 0 (t), with t max t min tdg 0 (t) < 1 t tdf 0(t). 15 The impact of the shock on the supplier s expected return is twofold. On the one hand, it lowers the probability that firms honor the trade credit contracts, reducing the supplier s expected return. On the other hand, Proposition 2 shows that the shock carries through to the updating done in response to a bank loan request, implying that the interest rate of a bank loan goes up to r B (G 1 ) = 1 pt min 1 > 1 pt 1 = rb (F 1 ). The shock, therefore, increases the value of the supplier s private information, allowing it to increase its profit margins. Of course, further restrictions on the distribution G 0 (t) are needed to determine the net effect of the shock on the supplier s expected profit. Nonetheless, our model predicts an unambiguously higher likelihood that the cost of trade credit varies with firm characteristics: The larger margin allowed by the higher bank rate makes it optimal for the supplier to increase the number of firms whose cost of trade credit varies with their probability of success. Proposition 4 formalizes the link between the equilibrium cost of trade credit and a negative shock that harms the economy s perspectives. Proposition 4 A shock that lowers the probability of success of all firms decreases ˆt(δ), increasing the fraction of firms whose cost of trade credit falls with the probability of success. Proposition 4 predicts that the cost of trade credit is more likely to vary with firm characteristics in industries plagued by economic distress. This implication of our model is consistent with Wilner (2000), who argues that suppliers have incentives to bail-out financially distressed customers in order to preserve long-term business relationships. Anticipating their own incentives, suppliers should embed the expected cost of the potential bail-out in the terms of trade credit. Clearly, this expected cost varies with the customer s risk and is more likely to be relevant in distressed industries. An example may help illustrate Propositions 3 and 4. The production function is Q(I) = I α, which implies an iso-elastic demand for inputs: ɛ(r) = 1, for any interest rate r. 1 α 15 A special case of the shock in the support of t is equivalent to an increase in the project-specific risk factor, that is, a lower p. To see this, let p > 0 be a small change in p that reduces the probability of success of a type-t firm to (p p)t. This probability of success can be written as ps = (p p)t, where s = 1 p p t is the shock in the space of types that is equivalent to the shock in p, if we consider that the new distribution ( of types is G 0 (s) = F p 0 p p ). s 14

This production function satisfies our technological assumptions if α (0, 1). To assure an equilibrium in which the cost of trade credit varies with firm characteristics, we also assume δ < 1 and 1 1 α = ɛ(rb ) > ɛ(r B, δ, 1) = p(1+r B )) 1 δ(1 p), or equivalently, α >. p(1+r B δ) (1 δ) p(1+r B ) From Proposition 2, ˆt(δ) is implicitly defined by ɛ(r B ) = ɛ(r B, δ, ˆt(δ)), which yields: ˆt(δ) = 1 δ p(α(1 + r B ) δ). (8) Equation (8) characterizes the safer firms that are offered trade credit contracts at a cost that decreases with the probability that the project succeeds, (ˆt(δ), 1], and the riskier firms that pay r B, regardless of their firm-specific factors, [t, ˆt(δ)]. A smaller value of ˆt(δ) increases the fraction of trade credit contracts whose interest rate varies with firm characteristics. As equation (8) shows, ˆt(δ) decreases with r B, which, in turn, increases with the expected probability that the project fails. Hence, the cost of trade credit is more likely to vary with firm characteristics in economically distressed industries. To see the impact of the salvage value δ on the cross-sectional variation of interest rates, differentiate ˆt(δ) with respect to δ to obtain dˆt(δ) dδ = p( α(1+rb )+1) (p(α(1+r B ) δ)) 2. One can check that dˆt(δ) dδ < 0 if and only if α > 1. This condition on α is implied by α > 1 δ(1 p), which assures that 1+r B p(1+r B ) the equilibrium allows for some trade credit contracts to vary with firm characteristics. 4 Trade credit and moral hazard problems Burkart and Ellingsen (2004) argue that trade credit is a pervasive source of external financing, because loans in kind are less vulnerable to opportunistic behavior. One may thus wonder whether moral hazard problems make it less likely that the cost of trade credit varies with firm-specific risk factors. To answer this question, we introduce a moral hazard problem in the investment decision that, in the spirit of Burkart and Ellingsen, weakens the bank s ability to compete with the supplier. 4.1 The moral hazard problem In this section, we expand the investment opportunities by letting the firms choose one of two mutually exclusive projects: R and S. 15

As in the single-project economy, projects R and S are risky. In case of success, the return of investing I in project i {R, S} is ρ i Q(I), where ρ i is a productivity parameter and Q(I) is an increasing and strictly concave production function that satisfies the Inada conditions. In case of failure, both projects leave a salvage value δi for the supplier while destroying the inputs when the bank is the source of external financing. By adding the firm-specific risk factors to those that are intrinsic to the projects, the probability of success of an investment by a firm t [t, 1] in project i {R, S} is p t i = tp i, with 1 > p S > p R > 0. To make the investment decision relevant for the firms, we assume that the value of project S is larger than the value of R, but, conditional on success, R delivers the highest return, that is, ρ S = 1 < ρ = ρ R. To be sure, a necessary condition for S to be the value-maximizing project is p S > ρp R. If failure destroys the initial investment (δ = 0), then any gap between p S and ρp R suffices for project S to maximize value. If δ > 0, a sufficient condition for S to be the efficient project is p S > ρp R with p R sufficiently close to zero. The assumptions on the productivity parameters give rise to a well known moral hazard problem identified by Jensen and Meckling (1976): Leverage induces firms to invest in the riskiest project. Despite the safest project s greater efficiency, a higher return in the successful states of nature creates incentive for the riskiest project R, because leverage keeps the upside gains in the firm while shifting part of the downside losses to the lender. The larger ρ is, the greater are the upside gains of project R and, consequently, the stronger are the incentives for the firms to inefficiently select the riskiest project. Accordingly, ρ parameterizes the strength of the moral hazard problem. As in Burkart and Ellingsen (2004), the supplier can mitigate moral hazard problems more efficiently than the bank, because trade credit is extended in kind. In particular, we assume that the supplier can tailor the inputs to the safest project. Trade credit contracts, therefore, can be contingent on the type of the firm and the choice of the project. In contrast, the bank may have to distort the loan contract in order to mitigate the moral hazard problem. 16

4.2 The optimal loan contract As Jensen and Meckling (1976) point out, leverage may induce firms to inefficiently select the riskiest project. Due to the verification cost, the best that the bank can do to mitigate the moral hazard problem is to offer a standard debt contract that satisfies three constraints. First, competition in the credit market implies that the debt contract cannot fetch a positive expected profit for the bank. Second, the contract must be profitable for the firms (participation constraint). And third, it must induce them to select the targeted project (incentive-compatibility constraint). To characterize the optimal loan contract, consider a standard debt contract that lends I S in exchange for the borrower s promise to pay A S when the project s payoff realizes. Once a firm seeks for a loan contract, the bank updates the prior distribution of types to F 1 (t). Given the updated belief, the loan contract leaves no expected profit for the bank if A S I S = 1 p S E 1 [t]. (9) Equation (9) implies that the promised return on the loan contract, r B S = A S I S 1, doesn t change with the amount of the loan. As such, we can write the loan contract as a pair (I S, r B S ). To characterize the loan amount I S, we move on to the incentive condition, which ties the loan to the efficient project, given by: p t S ] ] [Q(I S ) (1 + r BS )I S p t R [ρq(i S ) (1 + r BS )I S. (10) Inequality (10) assures that project S is more profitable than R, for any type-t firm that signs for the loan contract (I S, r B S ). After taking into account that p S > ρp R and p t i = tp i for i {R, S}, some simple algebra lets us write the incentive-compatibility condition, (10), as Q(I S ) I S (1 + r B S ) p S p R p S ρp R. (11) Condition (11) is a lower bound on the average productivity of the investment on the safest project. Since the production function is concave, average productivity decreases with the investment. Hence, the lower bound on the average productivity implies that the investment on the safe project cannot be larger than a cutoff call it ĪB S (ρ) that satisfies the restriction 17

(11) with equality. Proposition 5 shows that ĪB S (ρ) decreases with the moral hazard parameter ρ and that severe moral hazard problems implies credit constraint, that is, ĪB S (ρ) is smaller than the investment level I S (rb S ) that maximizes expected profits under the interest rate rb S.16 Proposition 5 A loan contract (I B S, rb S ) is incentive compatible if and only if IB S with dīb S (ρ) dρ ĪB S (ρ), < 0. Moreover, there is a productivity parameter ρ const ( 1, p S p R ) such that (I B S, r B S ) implies credit constraint if and only if ρ > ρ const. The intuition for Proposition 5 is straightforward. Firms lean towards the riskiest project if it delivers a large upside gain (high ρ). If these upside gains increase, the bank responds to the stronger moral hazard problem by reducing the credit line. In particular, the safest project becomes credit constrained once the productivity parameter ρ crosses the cut-off ρ const. If the incentive-compatible loan contract implies credit constraint, then the value of the safest project decreases relative to that of the riskiest project R. This raises the question of whether it is worthwhile for the bank to distort the loan contract to assure that the firm undertakes the safest project. Proposition 6 shows that the efficiency gains of inducing project S outweigh the cost of credit constraint, if the moral hazard problems are not too severe. 17 Proposition 6 There is a cutoff ρ S ( ρ const, p S p R ) such that an efficient loan contract induces the firms to undertake the safest project if and only if ρ ρ S. In the next section, we shall argue that the supplier, who is immune to the moral hazard problem, always ties trade credit to the safest project. As such, ρ > ρ S implies that the bank provides funding for the riskiest project, while the supplier finances the safest project. Conceivably, firms do not alter their investment plans simply because they have access to trade credit. We shall thus assume that ρ ρ S, from now on. This assumption, formalized below, implies that the credit line to the safest project is the equilibrium outcome in the market for bank loans. ] 16 More formally, ρ > ρ const implies that ĪB S (ρ) < I S (rb S ) = argmax Ip t S [Q(I) (1 + rs B)I. 17 The proof of Proposition 6 uses the fact that the bank cannot repossess the assets of bankrupted firms. Without this assumption, Proposition 6 holds if the elasticity of investment is bounded from above. 18

Assumption 2 The moral hazard parameter satisfies ρ ρ S. Hence, firms without trade credit undertake the safest project after borrowing from the bank. Assumption 2 does not necessarily imply credit constraint. Firms become credit constrained only if ρ (ρ const, ρ S ), in which case they borrow the maximum amount allowed by the bank, so that the scale of the project is as close as possible to the optimal investment IS (rb S ). We can therefore write the expected profit of the type-t firm with a bank loan as p t S [Q(I S (rbs )) (1 + rbs )I S (rbs ) ] if ρ ρ const, Π t B = p t SΠ B (ρ) p t S [Q(ĪBS (ρ)) (1 + rbs )ĪBS (ρ) ] if ρ (ρ const, ρ S ]. (12) Equation (12) characterizes the firms outside option in their bargaining with the supplier for trade credit. Equipped with it, we can turn our attention to the characterization of the optimal trade-credit contracts. 4.3 The optimal trade credit contracts The supplier s problem is to design a linear trade credit contract that maximizes its expected financial profit. To achieve this goal, the supplier takes into account its ability to tie the financing of the inputs to the project that maximizes the gains from trade, that is, project S. The best trade credit contract, therefore, is tied to a single project, as in the maximization program (5) that ignores moral hazard problems. While the supplier does not fear an inefficient selection of projects, the optimal trade credit contract is influenced by moral hazard problems in the market for bank loans. As Proposition 5 shows, severe moral hazard problems force the bank to constrain the supply of loans, weakening its ability to compete in the credit market. In response, the supplier can raise interest rates until the credit-constrained firms are indifferent between a cheaper (but undersized) bank loan and a larger (but costlier) trade credit offer. The maximum cost of trade credit that type-t firms are willing to pay call it r(ρ) is implicitly defined by p t S [ ] Q(IS( r(ρ))) (1 + r(ρ))is( r(ρ)) = Π t B. (13) 19

The left-hand side of equation (13) is the expected profit of a type-t firm that invests in project S, after accepting trade credit at the interest rate r(ρ). For r(ρ) to be the maximum interest rate that the supplier can charge, it must leave the firm s expected profit at its reservation value: the expected profit, Π t B, of borrowing from the bank to invest in project S (see equation (12)). If the type-t firm is not credit-constrained (ρ ρ const ), then the bank rate is the maximum interest rate that the supplier can charge (i.e., r(ρ) = rs B ). Otherwise, the supplier can raise r(ρ) above the bank rate. Not surprisingly, r(ρ) increases with ρ, because a stronger credit constraint (i.e., a larger ρ) increases firms willingness to pay for trade credit. We have thus established: Lemma 1 The cost of trade credit cannot be higher than the interest rate r(ρ) that is implicitly defined by equation (13). If the firm is not credit constrained (i.e., ρ ρ const ), then r(ρ) is the interest rate r B S of the bank loan designed to the safest project. Otherwise, r(ρ) strictly increases with the productivity parameter ρ, with r(ρ) > r B S, for any ρ > ρconst. From Lemma 1, we can write the supplier s problem as ( ) max p t S(1 + r t ) + (1 p t S)δ 1 IS(r t ) (14) r t ( 1 ) subject to (1 δ) 1 r t r(ρ). (15) p t S The objective function (14) is the expected financial profit of a trade credit contract. The maximization program has two constraints. The interest rate r t must be larger than the ( ) break-even point (1 δ) 1, but is capped by the maximum interest rate r(ρ) that the firm is willing to pay. 1 p t S A straightforward comparison of Programs (5) and (14) shows that the upper bound on the cost of trade credit, r(ρ) rs B, summarizes the impact of the moral hazard problem on the optimal trade credit contract: it may give more leeway for the supplier to raise interest rates. Moral hazard, therefore, does not change the essence of the supplier s problem. In particular, the optimal cost of trade credit is characterized by a first order condition that solves a trade off between margin of profit and volume of sales. As in Proposition 2, the first order condition of Program (14) implies that the supplier raises the cost of trade credit to the maximum rate r(ρ) if and only if the elasticity of demand at 20

r(ρ) is smaller than or equal to a cutoff, ɛ( r(ρ), δ, t) = tp S (1+ r(ρ)) tp S, which decreases with (1+ r(ρ) δ) (1 δ) the firm s type, t, and the salvage value δ. A sufficient condition for the cost of trade credit not to vary with firm characteristics is thus ɛ( r(ρ)) ɛ( r(ρ), δ, 1). If ɛ( r(ρ)) > ɛ( r(ρ), δ, 1) and δ < 1, then there is a cutoff type, ˆt(ρ, δ) [t, 1) such that r t = r(ρ) for any t [t, ˆt(ρ, δ)]. ( ) If t > ˆt(ρ, δ), then (1 δ) 1 < r t < r(ρ) and r t decreases with δ and t. 1 p t S In other words, the characterization of the equilibrium in Proposition 2 remains valid, provided that we substitute the interest rate r(ρ) for the bank rate rs B. As such, moral hazard problems change the equilibrium of the game in two ways only: it increases the cost of trade credit for the constrained firms, r(ρ) > rs B, and, as Proposition 7 below shows, decreases the cutoff type ˆt(ρ, δ) that splits the firms that pay r(ρ) from the firms whose cost of trade credit increases with firm-specific risk factors. Proposition 7 Let ˆt(ρ, δ) [t, 1] be the safest type that pays the interest rate r(ρ). Thus ˆt(ρ, δ) decreases with ρ and there is a cutoff value, ρ, such that ρ ρ implies that the cost of trade credit never varies with firm characteristics (i.e., ˆt(ρ, δ) = 1), in the unique sequential equilibrium of the game. If ρ > ρ and δ < 1, then the cost of trade credit decreases with the probability of success for any t ˆt(ρ, δ) > t. Intuitively, moral hazard problems weaken the bank s ability to provide financing, allowing the supplier to increase margins by raising interest rates. As we have already argued, large margins make the volume of loans more important for the supplier, strengthening its incentive to vary the interest rates with the borrowers risk of credit. Accordingly, Proposition 7 shows that stronger moral hazard problems (i.e., larger ρ) increase the the set of firms, (ˆt(ρ, δ), 1], whose cost of trade credit falls with the probability that the firm succeeds. As Jensen and Meckling (1976) point out, distressed firms have greater incentives to gamble with risky projects. Hence, Proposition 7 suggests that financially-distressed industries are likely places for empiricists to detect trade credit contracts with interest rates that vary with the borrower s creditworthiness. 18 18 In principle, financial distress could create moral hazard problems not only for the banks but also for the supplier. Nonetheless, Cuñat (2002) argues that suppliers are less vulnerable to moral hazard problems, because they can threaten to stop supplying vital intermediate goods. In this case, the suppliers are likely to be spared of moral hazard problems, making the banks the main targets of opportunistic behavior. 21

5 Discussion 5.1 A richer information structure for the bank In the basic model, the bank treats all firms equally. Everything works as if the bank couldn t distinguish, for instance, blue chip corporations from highly leveraged start-up companies. In this section, we endow the bank with a richer information structure and explore its impact on the equilibrium interest rates in the trade credit market. Consider a partition of the interval of types [t, 1], that is, a set of intervals {A k } K k=1 such that K k=1 A k = [t, 1] and A k A j =, for any k j. The partition is the outcome of public signals that cluster the firms in classes of risk: t < t for any t A k, t A l and l > k. With this information structure, the bank knows the prior distribution of each class of risk, but cannot identify the types of firms that belong to the same class. In this setting, Proposition 2 holds for each class of risk. In particular, the equilibrium bank rate in the class k is r B k = 1 pt k 1, where t k is the riskiest type in A k, that is, t k = min{t; t A k }. And the cost of trade credit for firms in the k th -class is the bank rate r B k, if the elasticity of demand at r B k is below a certain threshold. Of course, the same argument applies to firms in the class of risk A j with j k. If the demand for inputs is sufficiently inelastic, then the cost of trade credit for firms in A j is 1 pt j 1. But then 1 1 > 1 1 if and only if t pt j pt k j < t k, that is, the cost of trade credit is equal for firms in the same class of risk, but varies across classes. This pattern is consistent with the evidence that the cost of trade credit varies across industries but not with firm characteristics, if we interpret the partition of types as the set of industries in the economy. One may argue, nonetheless, that public signals convey information that help banks screen the credit risk of firms in a same industry. For instance, the risk of a short term loan to a cash-cow firm with no significant debt is negligible, possibly inducing the banks to offer lower interest rates that, ultimately, either rule out trade credit or force suppliers to lower interest rates. If these public signals are pervasive, our model predicts that the cost of trade credit is likely to vary not only across industries but also with firm characteristics. In contrast, our model predicts that suppliers are unlikely to vary interest rates with 22